Isn't check in from around 2 hours before take off and boarding anything from 1 hour down to 30 minutes before takeoff? I have known the boarding gates close 30 minutes before takeoff though if it's a busy flight. It's dependant on the airline and destination.

The gate might be open at 2pm but you are likely to still be going through security at that timeIt can take a while to clear security, so you really need to be planning on arriving 2-3 hours before your flight